Science:Math Exam Resources/Courses/MATH110/December 2015/Question 10 (b)

MATH110 December 2015

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[hide] Question 10 (b)

Upon the first snow fall of the year, your friends in Ontario always place a metre stick in their yard so they can measure how much snow they get throughout the winter. Their measurements for last year’s snow during the month of December are shown in the table below. Day in December 1 9 11 14 18 24 31 Amount of snow (cm) 19 8 23 14 34 29 33 (b) Your friends also tell you that right after making their measurement on December 1st, they were hit by a huge snow storm followed by a few days of uncharacteristically warm weather. How does this extra information change your answer to part(a)? Justify your answer.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

[show] Hint
Again apply IVT for the intervals close to the first day. How many times does the snow amount get to 20 cm when there is a decrease and an increase in the temperature?

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[show] Solution

The extra information implies that right after Dec 1 because of the huge snow storm the amount of snow will rise above $20$ cm, so again by IVT there is a day $c$ right after 1st day such that $f(c)=20$. Moreover, since the temperature would rise dramatically due to the warm weather, the snow height will go down below $20$ cm, this means that there is another $c$th day with $f(c)=20$. Therefore, there would be two more days close to Dec 1 at which the snow height is $20$ cm. Taking into account part (a), with this extra information, there would be at least $\color {blue}5$ days with the height of snow equal to 20 cm.